Resonator element having a pair of vibrating arms with wide portions and arm portions

ABSTRACT

A resonator element includes a base portion and a pair of vibrating arms that are provided integrally with the base portion, are aligned in an X-axis direction, and extend in a Y-axis direction from the base portion. Each of the vibrating arms includes an arm portion and a wide hammerhead that is located on the free end side of the arm portion and has a greater length in the X-axis direction than the arm portion. Assuming that the length of the vibrating arm in the Y-axis direction is L and the length of the hammerhead in the Y-axis direction is H, the relationship of 1.2%&lt;H/L&lt;30.0% is satisfied. Assuming that the length of the arm portion in the X-axis direction is W 1  and the length of the hammerhead in the X-axis direction is W 2 , the relationship of 1.5≦W 2 /W 1 ≦10.0 is satisfied.

This application is a Continuation of U.S. patent application Ser. No.14/202,596 filed Mar. 10, 2014, which is based upon and claims thebenefit of priority from Japanese Patent Application No. 2013-052489filed Mar. 14, 2013, the entire contents of the prior applications beingincorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to a resonator element, a resonator, anoscillator, an electronic apparatus, and a moving object.

2. Related Art

A resonator element using crystal is known. Such a resonator element hasan excellent frequency-temperature characteristic. Accordingly, theresonator element is widely used as a reference frequency source, asignal transmission source, or the like of various electronicapparatuses. The resonator element disclosed in JP-A-2011-19159 is of atuning fork type, and includes a base portion and a pair of vibratingarms extending from the base portion. In addition, in order to reducethe size and improve the vibration characteristics, a weight portion(wide portion) called a hammerhead is formed at the distal end of eachvibrating arm. For example, the length of the hammerhead is set to 30%or more of the total length of the vibrating arm in JP-A-2011-19159, andthe length of the hammerhead is set to 35% to 41% of the total length ofthe vibrating arm in JP-A-2011-199331 and JP-A-2012-129904. However, ifthe length of the hammerhead is too great for the total length of thevibrating arm as in JP-A-2011-19159, JP-A-2011-199331, andJP-A-2012-129904, when the vibrating arm bends and vibrates, a regionwhere the vibrating arm bends and deforms greatly, that is, a region ofan arm portion having a smaller width than the wide portion, which is aregion where electrically efficient excitation can be performed, isreduced. As a result, since the CI value of the resonator elementbecomes high, vibration loss is increased.

SUMMARY

An advantage of some aspects of the invention is to provide a resonatorelement, which can exhibit excellent vibration characteristics whilereducing an increase in the CI value, and a resonator, an oscillator, anelectronic apparatus, and a moving object that include the resonatorelement.

The invention can be implemented as the following application examples.

Application Example 1

This application example is directed to a resonator element including: abase portion; and a pair of vibrating arms that extend in a firstdirection from the base portion in plan view and are aligned along asecond direction crossing the first direction in plan view. Each of thevibrating arms includes an arm portion and a wide portion, which isdisposed on a side of the arm portion opposite to the base portion inplan view and which has a length along the second direction that isgreater than the arm portion in plan view. Assuming that a length of thevibrating arm along the first direction is L and a length of the wideportion along the first direction is H, a relationship of 1.2%<H/L<30.0%is satisfied. Assuming that a length of the arm portion along the seconddirection is W1 and a length of the wide portion along the seconddirection is W2, a relationship of 1.5≦W2/W1≦10.0 is satisfied.

With this configuration, it is possible to obtain the resonator elementcapable of exhibiting excellent vibration characteristics while reducingan increase in the CI value.

Application Example 2

In the resonator element according to the application example, it ispreferable that the L and the H satisfy a relationship of4.6%<H/L<22.3%.

With this configuration, it is possible to more effectively reduce anincrease in the CI value.

Application Example 3

In the resonator element according to the application example, it ispreferable that the W1 and the W2 satisfy a relationship of1.6≦W2/W1≦7.0.

With this configuration, it is possible to more effectively reduce anincrease in the CI value.

Application Example 4

In the resonator element according to the application example, it ispreferable that a bottomed groove extending along the first direction isprovided on a principal surface of the arm portion.

With this configuration, since it is possible to reduce thermoelasticloss, it is possible to exhibit more excellent vibrationcharacteristics.

Application Example 5

In the resonator element according to the application example, it ispreferable that the wide portion includes a main body, which isconnected to a side of the arm portion opposite to the base portion, anda protruding portion, which extends from the main body toward the baseportion of the arm portion so as to be spaced apart from the arm portionin plan view.

With this configuration, it is possible to increase the mass of the wideportion while suppressing the total length of the vibrating arm. Inother words, it is possible to make the arm portion long withoutreducing the mass effect of the wide portion.

Application Example 6

In the resonator element according to the application example, it ispreferable that the wide portion further includes a pair of connectingportions that connect the protruding portion and the arm portion to eachother and have a length along a third direction perpendicular to thefirst and second directions that is smaller than the arm portion and theprotruding portion.

With this configuration, it is possible to increase the mass of the wideportion while suppressing the total length of the vibrating arm. Inother words, it is possible to make the arm portion long withoutreducing the mass effect of the wide portion.

Application Example 7

In the resonator element according to the application example, it ispreferable that the base portion includes a width-decreasing portion, inwhich a length in the second direction gradually decreases as a distancefrom the vibrating arm increases, on a side opposite to a side where thevibrating arm extends.

With this configuration, since the vibration of the vibrating arm isoffset (reduced and absorbed), it is possible to reduce vibrationleakage. Therefore, the resonator element having excellent vibrationcharacteristics is obtained.

Application Example 8

In the resonator element according to the application example, it ispreferable that the resonator element includes a support portion that islocated between the pair of vibrating arms and extends along the firstdirection from the base portion.

By fixing the resonator element to the package through the supportportion, it is possible to further reduce the vibration leakage.

Application Example 9

In the resonator element according to the application example, it ispreferable that the resonator element includes a pair of support armsthat are connected to the base portion, extend along the firstdirection, and are aligned along the second direction with the pair ofvibrating arms interposed therebetween in plan view.

By fixing the resonator element to the package through both supportarms, it is possible to further reduce the vibration leakage.

Application Example 10

This application example is directed to a resonator including: theresonator element according to the application example described above;and a package in which the resonator element is housed.

With this configuration, it is possible to obtain the resonator withhigh reliability.

Application Example 11

This application example is directed to an oscillator including theresonator element according to the application example described aboveand an oscillation circuit electrically connected to the resonatorelement.

With this configuration, it is possible to obtain the oscillator withhigh reliability.

Application Example 12

This application example is directed to an electronic apparatusincluding the resonator element according to the application exampledescribed above.

With this configuration, it is possible to obtain the electronicapparatus with high reliability.

Application Example 13

This application example is directed to a moving object including theresonator element according to the application example described above.

With this configuration, it is possible to obtain the moving object withhigh reliability.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a plan view of a resonator element according to a firstembodiment of the invention.

FIG. 2A is a cross-sectional view taken along the line A-A of FIG. 1.

FIG. 2B is a cross-sectional view taken along the line B-B of FIG. 1.

FIG. 2C is a cross-sectional view taken along the line A-A of FIG. 1.

FIG. 2D is a cross-sectional view taken along the line B-B of FIG. 1.

FIGS. 3A and 3B are plan views illustrating the principle of vibrationleakage reduction.

FIG. 4 is a cross-sectional view of a vibrating arm illustrating heatconduction when the vibrating arm bends and vibrates.

FIG. 5 is a graph showing the relationship between the Q value and f/fm.

FIG. 6 is a perspective view showing the shape and the size of avibrating arm used in the simulation.

FIG. 7 is a perspective view illustrating the effective width.

FIGS. 8A and 8B are graphs showing the relationship between thehammerhead occupancy and the low R1 index.

FIG. 9 is a plan view of a resonator element according to a secondembodiment of the invention.

FIG. 10 is a plan view of a resonator element according to a thirdembodiment of the invention.

FIG. 11 is a plan view of a resonator element according to a fourthembodiment of the invention.

FIG. 12 is a plan view of a resonator element according to a fifthembodiment of the invention.

FIG. 13 is a plan view of a resonator element according to a sixthembodiment of the invention.

FIG. 14 is a plan view of a resonator element according to a seventhembodiment of the invention.

FIG. 15 is a plan view showing a resonator according to a preferredembodiment of the invention.

FIG. 16 is a cross-sectional view taken along the line C-C of FIG. 15.

FIG. 17 is a cross-sectional view showing an oscillator according to apreferred embodiment of the invention.

FIG. 18 is a perspective view showing the configuration of a mobile (ornotebook) personal computer as an electronic apparatus including theresonator element according to the embodiment of the invention.

FIG. 19 is a perspective view showing the configuration of a mobilephone (PHS is also included) as an electronic apparatus including theresonator element according to the embodiment of the invention.

FIG. 20 is a perspective view showing the configuration of a digitalstill camera as an electronic apparatus including the resonator elementaccording to the embodiment of the invention.

FIG. 21 is a perspective view schematically showing a vehicle as anexample of a moving object according to the invention.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, a resonator element, a resonator, an oscillator, anelectronic apparatus, and a moving object of the invention will bedescribed in detail by way of preferred embodiments shown in thediagrams.

1. Resonator Element

First, the resonator element according to the invention will bedescribed.

First Embodiment

FIG. 1 is a plan view of a resonator element according to a firstembodiment of the invention, FIG. 2A is a cross-sectional view takenalong the line A-A of FIG. 1, FIG. 2B is a cross-sectional view takenalong the line B-B of FIG. 1, FIGS. 3A and 3B are plan viewsillustrating the principle of vibration leakage reduction, FIG. 4 is across-sectional view of a vibrating arm illustrating heat conductionwhen the vibrating arm bends and vibrates, FIG. 5 is a graph showing therelationship between the Q value and f/fm, FIG. 6 is a perspective viewshowing the shape and size of a vibrating arm used in the simulation,FIG. 7 is a perspective view illustrating the effective width a, andFIGS. 8A and 8B are graphs showing the relationship between thehammerhead occupancy and the low R1 index. In addition, as shown in FIG.1, three axes perpendicular to each other are assumed to be an X axis(electrical axis of quartz crystal), a Y axis (mechanical axis of quartzcrystal), and a Z axis (optical axis of quartz crystal) hereinbelow forconvenience of explanation.

As shown in FIGS. 1, 2A, and 2B, a resonator element 2 includes a quartzcrystal substrate 3 and first and second driving electrodes 84 and 85formed on the quartz crystal substrate 3.

The quartz crystal substrate 3 is formed of a Z-cut quartz crystalplate. The Z-cut quartz crystal plate is a quartz crystal substratehaving a Z axis as its thickness direction. In addition, it ispreferable that the Z axis match the thickness direction of the quartzcrystal substrate 3. However, from the viewpoint of reducing thefrequency temperature change near the room temperature, the Z axis maybe inclined slightly (for example, less than about 15°) with respect tothe thickness direction.

That is, in a Cartesian coordinate system having an X axis as anelectrical axis, a Y axis as a mechanical axis, and a Z axis as anoptical axis of the crystal, assuming that an axis obtained by incliningthe Z axis so that a +Z side rotates in a −Y direction of the Y axiswith the X axis as a rotation axis is a Z′ axis and an axis obtained byinclining the Y axis so that a +Y side rotates in a +Z direction of theZ axis with the X axis as a rotation axis is a Y′ axis, the quartzcrystal substrate 3 in which a direction along the Z′ axis is thethickness direction and a surface including the X axis and the Y′ axisis the principal surface is obtained.

In addition, although the thickness D of the quartz crystal substrate 3is not limited in particular, it is preferable that the thickness D ofthe quartz crystal substrate 3 be less than 70 μm. By setting such anumerical range, for example, when the quartz crystal substrate 3 isformed by wet etching (patterning), it is possible to effectivelyprevent that an unnecessary portion (portion to be removed) remains in aboundary of a vibrating arm 5 and a base portion 4, a boundary of an armportion 51 and a hammerhead 59 to be described later, and the like.Therefore, it is possible to obtain the resonator element 2 capable ofeffectively reducing vibration leakage. From a different point of view,it is preferable that the thickness D be equal to or greater than about70 μm and equal to or less than about 300 μm. More preferably, it ispreferable that the thickness D be equal to or greater than about 100 μmand equal to or less than about 150 μm. By setting such a numericalrange, the first and second driving electrodes 84 and 85 can be widelyformed on the side surfaces (side surfaces 513, 514, 613, and 614 to bedescribed later) of the quartz crystal substrate 3. Accordingly, it ispossible to lower the CI value.

The quartz crystal substrate 3 includes the base portion 4 and a pair ofvibrating arms 5 and 6.

The base portion 4 has an approximate plate shape that spreads on the XYplane and has a thickness in the Z-axis direction. The base portion 4includes a portion (main body 41), which supports and connects thevibrating arms 5 and 6, and a width-decreasing portion 42 to reducevibration leakage.

The width-decreasing portion 42 is provided on the proximal side (sideopposite to a side on which the vibrating arms 5 and 6 extend) of themain body 41. In addition, the width (length along the X-axis direction)of the width-decreasing portion 42 gradually decreases as a distancefrom each of the vibrating arms 5 and 6 increases. Due to thewidth-decreasing portion 42, it is possible to effectively reduce thevibration leakage of the resonator element 2.

This will be specifically described as follows. In addition, in order tosimplify the explanation, it is assumed that the shape of the resonatorelement 2 is symmetrical with respect to a predetermined axis parallelto the Y axis.

First, as shown in FIG. 3A, a case where the width-decreasing portion 42is not provided will be described. When the vibrating arms 5 and 6 bendand deform so as to be spaced apart from each other, displacement closeto the clockwise rotational movement occurs as indicated by the arrow inthe main body 41 in the vicinity of a portion to which the vibrating arm5 is connected, and displacement close to the counterclockwiserotational movement occurs as indicated by the arrow in the main body 41in the vicinity of a portion to which the vibrating arm 6 is connected(strictly speaking, this movement cannot be said to be rotationalmovement; accordingly, this is expressed as “being close to therotational movement” for convenience). Since X-axis-direction componentsof these displacements are in the directions opposite to each other, theX-axis-direction components are offset in the X-axis-direction middleportion of the main body 41, and displacement in the +Y-axis directionremains (strictly speaking, displacement in the Z-axis direction alsoremains; however, the displacement in the Z-axis direction will beomitted herein). That is, the main body 41 bends and deforms such thatthe X-axis-direction middle portion is displaced in the +Y-axisdirection. When an adhesive is formed in the Y-axis-direction middleportion of the main body 41 having the above-described displacement inthe +Y-axis direction and the main body 41 is fixed to the packagethrough the adhesive, elastic energy due to the displacement in the+Y-axis direction leaks to the outside through the adhesive. This is theloss of vibration leakage, causing the degradation of the Q value. As aresult, the CI value is degraded.

In contrast, as shown in FIG. 3B, when the width-decreasing portion 42is provided, the width-decreasing portion 42 has an arch-shaped (curved)contour. For this reason, the displacements close to the rotationalmovement described above are applied to each other in thewidth-decreasing portion 42. That is, in the X-axis-direction middleportion of the width-decreasing portion 42, displacements in the X-axisdirection are offset as in the X-axis-direction middle portion of themain body 41, and the displacement in the Y-axis direction is alsosuppressed. In addition, since the contour of the width-decreasingportion 42 has an arch shape, the displacement in the +Y-axis directionthat is about to occur in the main body 41 is also suppressed. As aresult, the +Y-axis-direction displacement of the X-axis-directionmiddle portion of the base portion 4 when the width-decreasing portion42 is provided becomes much smaller than that when the width-decreasingportion 42 is not provided. That is, it is possible to obtain aresonator element having small vibration leakage.

In addition, although the contour of the width-decreasing portion 42 hasan arch shape herein, the shape of the contour of the width-decreasingportion 42 is not limited thereto as long as the operation describedabove can be realized. For example, it is possible to use awidth-decreasing portion having a contour that is formed stepwise by aplurality of straight lines.

The vibrating arms 5 and 6 are aligned in the X-axis direction (seconddirection), and extend in the Y-axis direction (first direction) fromthe upper end of the base portion 4 so as to be parallel to each other.Each of the vibrating arms 5 and 6 has a longitudinal shape. The baseend of each of the vibrating arms 5 and 6 is a fixed end, and the distalend is a free end. In addition, the vibrating arms 5 and 6 include armportions 51 and 61 and hammerheads (wide portions) 59 and 69 provided atthe distal ends of the arm portions 51 and 61.

The arm portion 51 has a pair of principal surfaces 511 and 512, whichare the XY plane, and a pair of side surfaces 513 and 514, which are theYZ plane and connect the pair of principal surfaces 511 and 512 to eachother. In addition, the arm portion 51 includes a bottomed groove 52opened to the principal surface 511 and a bottomed groove 53 opened tothe principal surface 512. Each of the grooves 52 and 53 extends in theY-axis direction, and its distal end extends up to the hammerhead 59 andits base end extends up to the base portion 4.

Thus, since it is possible to reduce thermoelastic loss by forming thegrooves 52 and 53 in the vibrating arm 5, it is possible to exhibitexcellent vibration characteristics (to be described in detail later).Since the length of each of the grooves 52 and 53 is not limited, thedistal end of each of the grooves 52 and 53 may not need to extend tothe hammerhead 59. In particular, when the distal end of each of thegrooves 52 and 53 extends to the hammerhead 59 as in the presentembodiment, a stress concentration occurring near the distal end of eachgroove is reduced. Therefore, a possibility of chipping or breakage thatoccurs when an impact is applied is reduced. In addition, since the baseend of each of the grooves and 53 extends to the base portion 4, thestress concentration in the boundary thereof is reduced. Therefore, apossibility of chipping or breakage that occurs when an impact isapplied is reduced.

Although the depth of each of the grooves 52 and 53 is not limited inparticular, it is preferable that the relationship of 60%≦(D1+D2)/D≦95%be satisfied assuming that the depth of the groove 52 is D1 and thedepth of the groove 53 is D2 (in the present embodiment, D1=D2). Since aheat transfer path becomes long by satisfying such a relationship, it ispossible to more effectively reduce thermoelastic loss in an adiabaticregion (to be described in detail later).

In addition, it is preferable to form the grooves 52 and 53 by adjustingthe positions of the grooves 52 and 53 in the X-axis direction withrespect to the position of the vibrating arm 5 so that thecross-sectional center of gravity of the vibrating arm 5 matches thecenter of the cross-sectional shape of the vibrating arm 5. In thiscase, since it is possible to reduce unnecessary vibration(specifically, oblique vibration having an out-of-plane component) ofthe vibrating arm 5, it is possible to reduce vibration leakage. Inaddition, in this case, since it is also possible to reduce driving forunnecessary vibration, a driving region is relatively increased.Therefore, it is possible to reduce the CI value.

In addition, assuming that the widths (lengths in the X-axis direction)of bank portions (principal surfaces aligned with the groove 52 alongthe width direction perpendicular to the longitudinal direction of thevibrating arm interposed therebetween) 511 a, which are located on bothsides of the groove 52 of the principal surface 511 in the X-axisdirection, and bank portions 512 a, which are located on both sides ofthe groove 53 of the principal surface 512 in the X-axis direction, areW3, it is preferable to satisfy the relationship of 0 μm<W3≦20 μm. Inthis case, the IC value of the resonator element 2 becomes sufficientlylow. In the numerical range described above, it is preferable to satisfythe relationship of 5 μm<W3≦9 μm. In this case, in addition to theeffects described above, it is possible to reduce thermoelastic loss. Inaddition, it is also preferable to satisfy the relationship of 0 μm<W3≦5μm. In this case, it is possible to further lower the CI value of theresonator element 2.

The hammerhead 59 has an approximately rectangular shape in XY planview. In addition, the hammerhead 59 includes a main body 591 connectedto the distal end of the arm portion 51, protruding portions 592 and 593that protrude toward the proximal side of the vibrating arm 5 from themain body 591, and thin portions (connecting portions) 594 and 595formed between the protruding portions 592 and 593 and the arm portion51.

The main body 591 has a width (length in the X-axis direction) greaterthan the arm portion 51, and protrudes to both sides in the X-axisdirection from the arm portion 51. A pair of protruding portions 592 and593 are located on both sides in the X-axis direction with the armportion 51 interposed therebetween. Each of the protruding portions 592and 593 is spaced apart from the arm portion 51 in the X-axis direction,and protrudes from the proximal-side outer edge of the main body 591 tothe proximal side of the vibrating arm 5.

The thin portion 594 is provided between the protruding portion 592 andthe arm portion 51 so as to connect the protruding portion 592 and thearm portion 51 to each other, and the thin portion 594 is thinner thanthe protruding portion 592 and the arm portion 51 (length of the thinportion 594 in the Z-axis direction is shorter than those of theprotruding portion 592 and the arm portion 51). Therefore, a bottomedgroove 596 a opened to one principal surface of the hammerhead 59 and abottomed groove 596 b opened to another principal surface of thehammerhead 59 are formed between the arm portion 51 and the protrudingportion 592. Similarly, the thin portion 595 is provided between theprotruding portion 593 and the arm portion 51 so as to connect theprotruding portion 593 and the arm portion 51 to each other, and thethin portion 595 is thinner than the protruding portion 593 and the armportion 51. Therefore, a bottomed groove 597 a opened to one principalsurface of the hammerhead 59 and a bottomed groove 597 b opened toanother principal surface of the hammerhead 59 are formed between thearm portion 51 and the protruding portion 593.

By forming the hammerhead 59 in such a configuration, it is possible toincrease the mass of the hammerhead 59 while suppressing the totallength L of the vibrating arm 5. In other words, when the total length Lof the vibrating arm 5 is fixed, it is possible to ensure that the armportion 51 is as long as possible without reducing the mass effect ofthe hammerhead 59. Therefore, it is possible to increase the width(length in the X-axis direction) of the vibrating arm 5 in order toobtain a desired resonance frequency (for example, 32.768 kHz). As aresult, since a heat transfer path to be described later becomes long,thermoelastic loss is reduced and the Q value is improved.

In addition, the center of the hammerhead 59 in the X-axis direction maybe slightly shifted from the center of the vibrating arm 5 in the X-axisdirection. In this case, since it is possible to reduce the vibration ofthe base portion 4 in the Z-axis direction that occurs due to twistingof the vibrating arm 5 when the vibrating arm 5 bends and vibrates, itis possible to suppress vibration leakage.

Until now, the vibrating arm 5 has been described. The vibrating arm 6has the same configuration as the vibrating arm 5. That is, the armportion 61 has a pair of principal surfaces 611 and 612, which are theXY plane, and a pair of side surfaces 613 and 614, which are the YZplane and connect the pair of principal surfaces 611 and 612 to eachother. In addition, the arm portion 61 includes a bottomed groove 62opened to the principal surface 611 and a bottomed groove 63 opened tothe principal surface 612. Each of the grooves 62 and 63 extends in theY-axis direction, and its distal end extends up to the hammerhead 69 andits base end extends up to the base portion 4.

The hammerhead 69 has an approximately rectangular shape in XY planview. In addition, the hammerhead 69 includes a main body 691 connectedto the distal end of the arm portion 61, protruding portions 692 and 693that protrude toward the proximal side of the vibrating arm 6 from themain body 691, and thin portions 694 and 695 formed between theprotruding portions 692 and 693 and the arm portion 61.

The main body 691 has a width (length in the X-axis direction) greaterthan the arm portion 61, and protrudes to both sides in the X-axisdirection from the arm portion 61. A pair of the protruding portions 692and 693 are located on both sides in the X-axis direction with the armportion 61 interposed therebetween. Each of the protruding portions 692and 693 is spaced apart from the arm portion 61 in the X-axis direction,and protrudes from the proximal-side outer edge of the main body 691 tothe proximal side of the vibrating arm 6. The thin portion 694 isprovided between the protruding portion 692 and the arm portion 61 so asto connect the protruding portion 692 and the arm portion 61 to eachother, and the thin portion 694 is thinner than the protruding portion692 and the arm portion 61. Therefore, a bottomed groove 696 a opened toone principal surface of the hammerhead 69 and a bottomed groove 696 bopened to another principal surface of the hammerhead 69 are formedbetween the arm portion 61 and the protruding portion 692. Similarly,the thin portion 695 is provided between the protruding portion 693 andthe arm portion 61 so as to connect the protruding portion 693 and thearm portion 61 to each other, and the thin portion 695 is thinner thanthe protruding portion 693 and the arm portion 61. Therefore, a bottomedgroove 697 a opened to one principal surface of the hammerhead 69 and abottomed groove 697 b opened to another principal surface of thehammerhead 69 are formed between the arm portion 61 and the protrudingportion 693.

By forming the hammerhead 69 in such a configuration, it is possible toincrease the mass of the hammerhead 69 while suppressing the totallength L of the vibrating arm 6. In other words, when the total length Lof the vibrating arm 6 is fixed, it is possible to ensure that the armportion 61 is as long as possible without reducing the mass effect ofthe hammerhead 69.

In addition, the center of the hammerhead 69 in the X-axis direction maybe slightly shifted from the center of the vibrating arm 5 in the X-axisdirection. In this case, since it is possible to reduce the vibration ofthe base portion 4 in the Z-axis direction that occurs due to twistingof the vibrating arm 5 when the vibrating arm 5 bends and vibrates, itis possible to suppress vibration leakage.

As shown in FIGS. 2A and 2B, a pair of first driving electrodes 84 and apair of second driving electrodes 85 are formed in the vibrating arm 5.Specifically, one of the first driving electrodes 84 is formed on theinner surface (side surface) of the groove 52, and the other firstdriving electrode 84 is formed on the inner surface (side surface) ofthe groove 53. In addition, one of the second driving electrodes 85 isformed on the side surface 513, and the other second driving electrode85 is formed on the side surface 514. In addition, when the firstdriving electrode 84 is not formed so as to extend to a regionsurrounded by the hammerhead 59 or/and the second driving electrode 85does not extend from the side surface 513 to the inner surface (sidesurface on the arm portion 51 side) of the grooves 596 a and 596 b, theequivalent series capacitance C1 can be reduced. Accordingly, since theabsolute value of the load capacity sensitivity S (=C1/(2×(C0+CL)²) isreduced, it is possible to obtain the stable resonance characteristics.In addition, the load capacity sensitivity S is an index indicating achange in the resonance frequency with respect to a change in the loadcapacity, C0 is an electrostatic capacitance, and CL is a load capacity.

In addition, one second driving electrode 85 may extend from the sidesurface 513 to the inner surface (side surface on the arm portion 51side) of the grooves 596 a and 596 b. Similarly, the other seconddriving electrode 85 may extend from the side surface 514 to the innersurface (side surface on the arm portion 51 side) of the grooves 597 aand 597 b. In this case, it is possible to make a region where theelectric field is applied wider.

Similarly, a pair of first driving electrodes 84 and a pair of seconddriving electrodes 85 are also formed in the vibrating arm 6.Specifically, one of the first driving electrodes 84 is formed on theside surface 613, and the other first driving electrodes 84 is formed onthe side surface 614. In addition, one of the second driving electrodes85 is formed on the inner surface (side surface) of the groove 62, andthe other second driving electrodes 85 is formed on the inner surface(side surface) of the groove 63. In addition, one first drivingelectrode 84 may extend from the side surface 613 to the inner surface(side surface on the arm portion 61 side) of the grooves 696 a and 696b. Similarly, the other first driving electrode 84 may extend from theside surface 614 to the inner surface (side surface on the arm portion61 side) of the grooves 697 a and 697 b. In this case, it is possible tomake a region where the electric field is applied wider.

When an AC voltage is applied between the first and second drivingelectrodes 84 and 85, the vibrating arms 5 and vibrate at apredetermined frequency in the in-plane direction (XY plane direction)so as to repeat being close to and away from each other.

Materials of the first and second driving electrodes 84 and 85 are notlimited in particular, and it is possible to use metal materials, suchas gold (Au), a gold alloy, platinum (Pt), aluminum (Al), an aluminumalloy, silver (Ag), a silver alloy, chromium (Cr), a chromium alloy,nickel (Ni), a nickel alloy, copper (Cu), molybdenum (Mo), niobium (Nb),tungsten (W), iron (Fe), titanium (Ti), cobalt (Co), zinc (Zn), andzirconium (Zr), and conductive materials, such as indium tin oxide(ITO).

As a specific configuration of the first and second driving electrodes84 and 85, it is possible to adopt a configuration in which an Au layerof 700 Å or less is formed on a Cr layer of 700 Å or less, for example.In particular, in the case of Cr or Au, thermoelastic loss is large.Therefore, the Cr layer and the Au layer are preferably equal to or lessthan 100 Å. In addition, since Ni has a thermal expansion coefficientclose to the thermal expansion coefficient of the crystal, thermalstress due to electrodes is reduced by forming a Ni layer as a baselayer in place of the Cr layer. In this case, it is possible to obtain aresonator element with good long-term reliability (agingcharacteristics).

As described above, in the resonator element 2, it is possible to reducethermoelastic loss by forming the grooves 52, 53, 62, and 63 in thevibrating arms 5 and 6. Hereinafter, this will be specifically describedwith the vibrating arm 5 as an example.

As described above, the vibrating arm 5 bends and vibrates in thein-plane direction by applying an AC voltage between the first andsecond driving electrodes 84 and 85. As shown in FIG. 4, when thevibrating arm 5 bends and vibrates, the side surface 514 expands if theside surface 513 of the arm portion 51 contracts. In contrast, if theside surface 513 expands, the side surface 514 contracts. When thevibrating arm 5 does not cause the Gough-Joule effect (when energyelasticity is dominant over the entropy elasticity), the temperature onthe contracted surface side of the side surfaces 513 and 514 rises, andthe temperature on the expanded surface side drops. For this reason, atemperature difference occurs between the side surfaces 513 and 514(that is, inside the arm portion 51). Due to heat conduction resultingfrom such a temperature difference, loss of vibration energy occurs. Asa result, the Q value of the resonator element 2 is reduced. Such areduction in the Q value is also called a thermoelastic effect, and theloss of energy due to the thermoelastic effect is also calledthermoelastic loss.

In a resonator element that vibrates in a bending vibration mode and hasthe same configuration as the resonator element 2, when the bendingvibration frequency (mechanical bending vibration frequency) f of thevibrating arm 5 changes, the Q value is minimized when the bendingvibration frequency of the vibrating arm 5 matches a thermal relaxationfrequency fm. The thermal relaxation frequency fm can be calculated byfm=1/(2πτ) (where π is the circumference ratio, and τ is relaxation timerequired for the temperature difference to become e⁻¹ times due to heatconduction, assuming that e is Napier's constant).

In addition, assuming that the thermal relaxation frequency of the flatplate structure (structure having a rectangular cross-sectional shape)is fm0, fm0 can be calculated by the following expression.

fm0=πk/(2ρCpa ²)  (1)

In addition, η is the circumference ratio, k is the thermal conductivityin the vibration direction of the vibrating arm 5, ρ is the mass densityof the vibrating arm 5, Cp is the heat capacity of the vibrating arm 5,and a is the width of the vibrating arm 5 in the vibration direction.When the constant of the material itself (that is, crystal) of thevibrating arm 5 is input to the thermal conductivity k, the mass densityρ, and the heat capacity Cp in Expression (1), the calculated thermalrelaxation frequency fm0 is a value when the grooves 52 and 53 are notprovided in the vibrating arm 5.

In the vibrating arm 5, the grooves 52 and 53 are formed so as to belocated between the side surfaces 513 and 514. For this reason, since aheat transfer path for balancing the temperature by eliminating thetemperature difference between the side surfaces 513 and 514, which iscaused when the vibrating arm 5 bends and vibrates, by heat conductionis formed so as to bypass the grooves 52 and 53, the heat transfer pathis longer than the straight-line distance (shortest distance) betweenthe side surfaces 513 and 514. Therefore, compared with a case where thegrooves 52 and 53 are not provided in the vibrating arm 5, therelaxation time τ becomes long, and the thermal relaxation frequency fmbecomes low.

FIG. 5 is a graph showing the f/fm dependence of the Q value of theresonator element in the bending vibration mode. In FIG. 5, a curve F1indicated by the dotted line shows a case where a groove is formed in avibrating arm as in the resonator element 2 (case where thecross-sectional shape of the vibrating arm is an H shape), and a curveF2 indicated by the solid line shows a case where no groove is formed ina vibrating arm (case where the cross-sectional shape of a connectingarm is a rectangle). As shown in FIG. 5, the shapes of the curves F1 andF2 are not changed, but the curve F1 is shifted in a frequency decreasedirection with respect to the curve F2 with a reduction in the thermalrelaxation frequency fm as described above. Accordingly, assuming thatthe thermal relaxation frequency when a groove is formed in a vibratingarm as in the resonator element 2 is fm1, the Q value of the resonatorelement in which a groove is formed in the vibrating arm is alwayshigher than the Q value of the resonator element in which no groove isformed in the vibrating arm by satisfying the following Expression (2).

f>√{square root over (f _(m0) f _(m1))}  (2)

In addition, it is possible to obtain a higher Q value when beinglimited to the relationship of f/fm0>1.

In addition, in FIG. 5, the region of f/fm<1 is also called anisothermal region. In this isothermal region, the Q value increases asf/fm decreases. This is because it is difficult for the above-describedtemperature difference in the vibrating arm to occur as the mechanicalfrequency of the vibrating arm becomes low (vibration of the vibratingarm becomes slow). Accordingly, in a limit when f/fm approaches 0 (zero)infinitely, an isothermal quasi-static operation is realized, andthermoelastic loss approaches 0 (zero) infinitely. Meanwhile, the regionof f/fm>1 is also called an adiabatic region. In this adiabatic region,the Q value increases as f/fm increases. This is because the switchingof temperature rise and temperature effect of each side surface becomesfast as the mechanical frequency of the vibrating arm becomes high, andaccordingly, there is no time in which the above-described heatconduction occurs. Accordingly, in a limit when f/fm is increasedinfinitely, an adiabatic operation is realized, and thermoelastic lossapproaches 0 (zero) infinitely. From this, it can be rephrased that f/fmis in the adiabatic region if the relationship of f/fm>1 is satisfied.

Next, the relationship between the total length of the vibrating arms 5and 6 and the length and width of the hammerheads 59 and 69 will bedescribed. Since the vibrating arms 5 and 6 have the same configuration,the vibrating arm will be described as a representative vibrating armhereinafter, and explanation of the vibrating arm 6 will be omitted.

As shown in FIG. 1, assuming that the total length (length in the Y-axisdirection) of the vibrating arm 5 is L and the length (length in theY-axis direction) of the hammerhead 59 is H, the vibrating arm 5satisfies the relationship of 1.2%<H/L<30.0%. If this relationship issatisfied, it is preferable that the relationship of 4.6%<H/L<22.3% befurther satisfied, even though the relationship is not limited inparticular. When such a relationship is satisfied, the CI value of theresonator element 2 can be kept low. Therefore, since the vibration lossis small, the resonator element 2 having excellent vibrationcharacteristics is obtained. Here, in the present embodiment, the baseend of the vibrating arm 5 is set in a position of the line segment,which connects a place where the side surface 514 is connected to thebase portion 4 and a place where the side surface 513 is connected tothe base portion 4, in the middle of the width (length in the X-axisdirection) of the vibrating arm 5.

In addition, assuming that the width (length in the X-axis direction) ofthe arm portion 51 is W1 and the width (length in the X-axis direction)of the hammerhead 59 is W2, the vibrating arm 5 satisfies therelationship of 1.5≦W2/W1≦10.0. If this relationship is satisfied, it ispreferable that the relationship of 1.6≦W2/W1≦7.0 be further satisfied,even though the relationship is not limited in particular. By satisfyingsuch a relationship, it is possible to ensure the great width of thehammerhead 59. Therefore, even if the length H of the hammerhead 59 isrelatively small as described above (even if the length H of thehammerhead 59 is less than 30% of L), it is possible to sufficientlyexhibit the mass effect of the hammerhead 59. Therefore, by satisfyingthe relationship of 1.5≦W2/W1≦10.0, the total length L of the vibratingarm 5 is reduced. As a result, it is possible to reduce the size of theresonator element 2.

Thus, the vibrating arm 5 satisfies the relationship of 1.2%<H/L<30.0%and the relationship of 1.5≦W2/W1≦10.0. By the synergetic effect ofthese two relationships, the resonator element 2 that is small and has asufficiently reduced CI value is obtained.

In addition, by setting L≦2 mm, preferably, L≦1 mm, it is possible toobtain a small resonator element used in an oscillator that is mountedin a portable music device, an IC card, and the like. In addition, bysetting W1≦100 μm, preferably, W1≦50 μm, it is also possible to obtain aresonator element, which resonates at a low frequency and which is usedin an oscillation circuit for realizing low power consumption, in therange of L. In addition, in the case of an adiabatic region, when thevibrating arm extends in the Y direction in the crystal Z plate andbends and vibrates in the X direction, it is preferable that W1≦12.8 μmbe satisfied. When the vibrating arm extends in the X direction in thecrystal Z plate and bends and vibrates in the Y direction, it ispreferable that W1≦14.4 μm be satisfied. When the vibrating arm extendsin the Y direction in the crystal X plate and bends and vibrates in theZ direction, it is preferable that W1≦15.9 μm be satisfied. In thiscase, since an adiabatic region can be reliably obtained, thermoelasticloss is reduced by the formation of a groove, and the Q value isimproved. In addition, due to driving in a region where a groove isformed, the electric field efficiency is high, and the driving area issecured. Accordingly, the CI value is reduced.

Next, on the basis of a simulation result, it will be proved that theabove-described effect can be exhibited by satisfying the relationshipof 1.2%<H/L<30.0% and the relationship of 1.5≦W2/W1≦10.0. Thissimulation was performed using one vibrating arm 5. In addition, thevibrating arm 5 used in this simulation is formed of a crystal Z plate(rotation angle of 0°). In this simulation, as the size of the vibratingarm 5, as shown in FIG. 6, the total length L is 1210 μm and thethickness D is 100 μm, the width W1 of the arm portion 51 is 98 μm, thewidth W2 of the hammerhead 59 is 172 μm, the depths D1 and D2 of thegrooves 52 and 53 are 45 μm, and the width W3 of each of the bankportions 511 a and 512 a is 6.5 μm. Simulation was performed whilechanging the length H of the hammerhead 59 of the vibrating arm 5. Inaddition, the present inventors confirmed that a result similar to thesimulation result shown below was obtained even if the size (L, W1, W2,D, D1, D2, and W3) of the vibrating arm 5 was changed.

The following Table 1 is a table indicating a CI value change when thelength H of the hammerhead 59 is changed. In addition, in thissimulation, the CI value of each sample is calculated as follows. First,the Q value when only the thermoelastic loss is considered is calculatedusing the finite element method. Then, since the Q value isfrequency-dependent, the calculated Q value is converted into the Qvalue at the time of 32.768 kHz (Q value after F conversion). Then, R1(CI value) is calculated on the basis of the Q value after F conversion.Then, since the CI value is also frequency-dependent, the calculated R1is converted into R1 at the time of 32.768 kHz and the reciprocal istaken as a “low R1 index”. The low R1 index is an index when areciprocal, which is the greatest in all simulations, is set to 1.Therefore, as the low R1 index becomes close to 1, the CI valuedecreases. FIG. 8A shows a graph in which the hammerhead occupancy (H/L)is plotted on the horizontal axis and the low R1 index is plotted on thevertical axis, and FIG. 8B shows a graph obtained by enlarging a part ofFIG. 8A.

In addition, a method of converting the Q value to the Q value after Fconversion is as follows.

The following calculation was performed using the following Expressions(3) and (4).

f ₀ =πk/(2ρCpa ²)  (3)

Q={ρCp/(Cα ² H)}×[{1+(f/f ₀)²}/(f/f ₀)]  (4)

In Expressions (3) and (4), π is the circumference ratio, k is thethermal conductivity of the vibrating arm 5 in the width direction, ρ isa mass density, Cp is a heat capacity, C is an elastic stiffnessconstant of expansion and contraction in the length direction of thevibrating arm 5, α is a thermal expansion coefficient of the vibratingarm 5 in the length direction, H is an absolute temperature, and f is anatural frequency. In addition, a is a width (effective width) when thevibrating arm 5 is regarded as a flat plate shape shown in FIG. 7. Inaddition, although the grooves 52 and 53 are not formed in the vibratingarm 5 in FIG. 7, it is possible to perform conversion into the Q valueafter F conversion even if the value of “a” in this case is used.

First, the natural frequency of the vibrating arm 5 used in thesimulation is set to F1 and the calculated Q value is set to Q1, and thevalue of “a” satisfying f=F1 and Q=Q1 is calculated using Expressions(3) and (4). Then, using the calculated “a” and f=32.768 kHz, the valueof Q is calculated from Expression (2). The Q value obtained in thismanner is the Q value after F conversion.

TABLE 1 Natural frequency Q value after H/L F1 [Hz] Q1 F conversion R1[Ω] 1/R1 Low R1 index SIM001 0.6% 7.38E+04 159.398 76.483 3.50E+031.270E−04 0.861 SIM002 3.3% 5.79E+04 135.317 76.606 4.15E+03 1.363E−040.923 SIM003 6.0% 4.99E+04 120.906 79.442 4.58E+03 1.435E−04 0.972SIM004 8.6% 4.48E+04 111.046 81.157 4.98E+03 1.467E−04 0.994 SIM00511.2% 4.13E+04 103.743 82.223 5.37E+03 1.476E−04 1.000 SIM006 13.9%3.88E+04 98.038 82.843 5.74E+03 1.471E−04 0.997 SIM007 16.5% 3.68E+0493.507 83.225 6.10E+03 1.458E−04 0.988 SIM008 19.8% 3.49E+04 88.85683.328 6.56E+03 1.430E−04 0.969 SIM009 23.1% 3.35E+04 85.017 83.1157.02E+03 1.393E−04 0.944 SIM010 26.4% 3.24E+04 81.772 82.657 7.50E+031.348E−04 0.914 SIM011 29.8% 3.16E+04 78.811 81.824 8.01E+03 1.296E−040.878 SIM012 33.1% 3.09E+04 76.247 80.864 8.56E+03 1.239E−04 0.839SIM013 36.4% 3.04E+04 73.813 79.591 9.17E+03 1.176E−04 0.796 SIM01439.7% 3.00E+04 71.409 77.963 9.87E+03 1.106E−04 0.749 SIM015 43.0%2.98E+04 69.077 76.078 1.07E+04 1.032E−04 0.699 SIM016 46.3% 2.96E+0466.818 73.978 1.16E+04 9.557E−05 0.648 SIM017 49.6% 2.95E+04 64.44971.494 1.27E+04 8.750E−05 0.593 SIM018 52.9% 2.96E+04 62.042 68.7331.40E+04 7.928E−05 0.537 SIM019 56.2% 2.97E+04 59.670 65.800 1.55E+047.104E−05 0.481 SIM020 59.5% 3.00E+04 57.018 62.370 1.75E+04 6.257E−050.424 SIM021 62.8% 3.03E+04 54.502 58.918 1.98E+04 5.447E−05 0.369SIM022 66.1% 3.08E+04 51.676 54.983 2.29E+04 4.640E−05 0.314 SIM02369.4% 3.14E+04 48.788 50.857 2.69E+04 3.871E−05 0.262 SIM024 72.7%3.23E+04 45.699 46.416 3.23E+04 3.140E−05 0.213 SIM025 76.0% 3.33E+0442.398 41.687 4.00E+04 2.461E−05 0.167 SIM026 79.3% 3.47E+04 39.08436.902 5.08E+04 1.857E−05 0.126 SIM027 82.6% 3.65E+04 35.523 31.8726.77E+04 1.325E−05 0.090 SIM028 85.5% 3.86E+04 32.226 27.387 9.12E+049.314E−06 0.063 SIM029 88.3% 4.13E+04 28.763 22.842 1.31E+05 6.056E−060.041 SIM030 91.1% 4.50E+04 24.918 18.132 2.11E+05 3.448E−06 0.023SIM031 93.9% 5.07E+04 21.042 13.614 4.04E+05 1.602E−06 0.011

The present inventors require the resonator element 2 having the low R1index of 0.87 or more. As can be seen from Table 1 and the graphs ofFIGS. 8A and 8B, the low R1 index is equal to or greater than a targetof 0.87 if the relationship of 1.2%<H/L<30.0% is satisfied (SIM002 toSIM011). In particular, if the relationship of 4.6%<H/L<22.3% issatisfied (SIM003 to SIM008), the low R1 index exceeds 0.95. Therefore,it can be seen that the CI value is further reduced. From the abovesimulation result, it was proved that the resonator element 2 having asufficiently reduced CI value was obtained by satisfying therelationship of 1.2%<H/L<30.0%.

Second Embodiment

Next, a resonator element according to a second embodiment of theinvention will be described.

FIG. 9 is a plan view of the resonator element according to the secondembodiment of the invention.

Hereinafter, the resonator element of the second embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the second embodiment of theinvention is the same as that of the first embodiment described aboveexcept that the configuration of a hammerhead is different. In addition,the same components as in the first embodiment described above aredenoted by the same reference numerals.

As shown in FIG. 9, a hammerhead 59A includes a main body 591 connectedto the distal end of an arm portion 51 and protruding portions 592 and593 that protrude toward the proximal side of a vibrating arm 5 from themain body 591. That is, the hammerhead 59A is formed by omitting thethin portions 594 and 595 from the hammerhead 59 of the first embodimentdescribed above. By forming the hammerhead 59A in such a configuration,it is possible to increase the mass of the hammerhead 59A whilesuppressing the total length L of the vibrating arm 5. In other words,when the total length L of the vibrating arm 5 is fixed, it is possibleto ensure that the arm portion 51 is as long as possible withoutreducing the mass effect of the hammerhead 59A. Therefore, it ispossible to increase the width (length in the X-axis direction) of thevibrating arm 5 in order to obtain a desired resonance frequency (forexample, 32.768 kHz). As a result, since the heat transfer pathdescribed above becomes long, thermoelastic loss is reduced and the Qvalue is improved. Here, as shown in FIG. 9, the length H of thehammerhead 59A is from a connecting portion between the hammerhead 59Aand the arm portion 51 to the free end, and the length of the protrudingportion 592 or 593 is not included in the length H. In addition, thefree end portion of the arm portion 51 has a tapered shape whose widthincreases gradually toward the free end. When the arm portion 51 has aportion in which the width (length in the X-axis direction) of thetapered portion is 1.5 times or more of the width (length in the X-axisdirection) of the arm portion 51, this portion is also included in thelength H.

Since the hammerhead 69A has the same configuration as the hammerhead59A described above, explanation thereof will be omitted.

Also in the second embodiment, the same effects as in the firstembodiment described above can be achieved.

Third Embodiment

Next, a resonator element according to a third embodiment of theinvention will be described.

FIG. 10 is a plan view of the resonator element according to the thirdembodiment of the invention.

Hereinafter, the resonator element of the third embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the third embodiment of the inventionis the same as that of the first embodiment described above except thatthe configuration of a hammerhead is different. In addition, the samecomponents as in the first embodiment described above are denoted by thesame reference numerals.

As shown in FIG. 10, in a hammerhead 59B, thin portions 594B and 595Bare shorter than the protruding portions 592 and 593, and only portionsof the protruding portions 592 and 593 on the fixed end side areconnected to the arm portion 51 through the thin portions 594B and 595B.By forming the hammerhead 59B in such a configuration, it is possible toincrease the mass of the hammerhead 59B while suppressing the totallength L of the vibrating arm 5. In other words, when the total length Lof the vibrating arm 5 is fixed, it is possible to ensure that the armportion 51 is as long as possible without reducing the mass effect ofthe hammerhead 59B. Therefore, it is possible to increase the width(length in the X-axis direction) of the vibrating arm 5 in order toobtain a desired resonance frequency (for example, 32.768 kHz). As aresult, since the heat transfer path described above becomes long,thermoelastic loss is reduced and the Q value is improved. Here, asshown in FIG. 10, the length H of the hammerhead 59B is from aconnecting portion between each of the thin portions 594B and 595B andthe arm portion 51 to the free end, and the length of a free end portionof each of the protruding portions 592 and 593 is not included in thelength H. In addition, the free end portion of the arm portion 51 has atapered shape whose width increases gradually toward the free end. Whenthe arm portion 51 has a portion in which the width (length in theX-axis direction) of the tapered portion is 1.5 times or more of thewidth (length in the X-axis direction) of the arm portion 51, thisportion is also included in the length H.

Since the hammerhead 69B has the same configuration as the hammerhead59B described above, explanation thereof will be omitted.

Also in the third embodiment, the same effects as in the firstembodiment described above can be achieved.

Fourth Embodiment

Next, a resonator element according to a fourth embodiment of theinvention will be described.

FIG. 11 is a plan view of the resonator element according to the fourthembodiment of the invention.

Hereinafter, the resonator element of the fourth embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the fourth embodiment of theinvention is the same as that of the first embodiment described aboveexcept that the configuration of a hammerhead is different. In addition,the same components as in the first embodiment described above aredenoted by the same reference numerals.

As shown in FIG. 11, a hammerhead 59C has an approximately rectangularshape, and is formed by omitting the protruding portions 592 and 593 andthe thin portions 594 and 595 from the hammerhead of the firstembodiment described above. By adopting such a configuration, theconfiguration of the hammerhead 59C becomes simple. In addition, thedistal end of each of the grooves 52 and 53 is located in a boundary ofthe arm portion 51 and the hammerhead 59C. The free end portion of thearm portion 51 has a tapered shape whose width increases graduallytoward the free end. When the arm portion 51 has a portion in which thewidth (length in the X-axis direction) of the tapered portion is 1.5times or more of the width (length in the X-axis direction) of the armportion 51, this portion is also included in the length H of thehammerhead 59C.

Since the hammerhead 69C has the same configuration as the hammerhead59C described above, explanation thereof will be omitted.

Also in the fourth embodiment, the same effects as in the firstembodiment described above can be achieved.

Fifth Embodiment

Next, a resonator element according to a fifth embodiment of theinvention will be described.

FIG. 12 is a plan view of the resonator element according to the fifthembodiment of the invention.

Hereinafter, the resonator element of the fifth embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the fifth embodiment of the inventionis the same as that of the first embodiment described above except thatthe configuration of a hammerhead is different. In addition, the samecomponents as in the first embodiment described above are denoted by thesame reference numerals.

As shown in FIG. 12, a hammerhead 59D has an approximately rectangularshape, and is formed by omitting the protruding portions 592 and 593 andthe thin portions 594 and 595 from the hammerhead of the firstembodiment described above. By adopting such a configuration, theconfiguration of the hammerhead 59D becomes simple. The free end portionof the arm portion 51 has a tapered shape whose width increasesgradually toward the free end. When the arm portion 51 has a portion inwhich the width (length in the X-axis direction) of the tapered portionis 1.5 times or more of the width (length in the X-axis direction) ofthe arm portion 51, this portion is also included in the length H of thehammerhead 59D.

Since the hammerhead 69D has the same configuration as the hammerhead59D described above, explanation thereof will be omitted.

Also in the fifth embodiment, the same effects as in the firstembodiment described above can be achieved.

Sixth Embodiment

Next, a resonator element according to a sixth embodiment of theinvention will be described.

FIG. 13 is a plan view of the resonator element according to the sixthembodiment of the invention.

Hereinafter, the resonator element of the sixth embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the sixth embodiment of the inventionis the same as that of the first embodiment described above except thata support portion is further provided. In addition, the same componentsas in the first embodiment described above are denoted by the samereference numerals.

As shown in FIG. 13, a resonator element 2E is located between vibratingarms 5 and 6, and includes a support portion 7 that extends in theY-axis direction from the base portion 4. Although not shown, theresonator element 2E is fixed to the package through an adhesive by thesupport portion 7. By adopting such a configuration, it is possible tomore effectively reduce the vibration leakage of the resonator element2E.

Also in the sixth embodiment, the same effects as in the firstembodiment described above can be achieved.

Seventh Embodiment

Next, a resonator element according to a seventh embodiment of theinvention will be described.

FIG. 14 is a plan view of the resonator element according to the seventhembodiment of the invention.

Hereinafter, the resonator element of the seventh embodiment will bedescribed focusing on the differences from the first embodimentdescribed above, and explanation of the same matters will be omitted.

The resonator element according to the seventh embodiment of theinvention is the same as that of the first embodiment described aboveexcept that a support portion is further provided. In addition, the samecomponents as in the first embodiment described above are denoted by thesame reference numerals.

As shown in FIG. 14, a resonator element 2F includes a support portion 7extending from a base portion 4. The support portion 7 includes a branchportion 71 that extends from the lower end (side opposite to aside wherethe vibrating arms 5 and 6 extend) of the base portion 4 and is branchedin the X-axis direction, connecting arms 72 and 73 extending from thebranch portion to both sides in the X-axis direction, and support arms74 and 75 extending from the distal ends of the connecting arms 72 and73 to the vibrating arms 5 and 6 in the Y-axis direction. In addition,the support arms 74 and 75 are disposed so as to face each other in theX-axis direction with the vibrating arms 5 and 6 interposedtherebetween. Although not shown, the resonator element 2F is fixed tothe package through an adhesive or the like by the support arms 74 and75. By adopting such a configuration, it is possible to more effectivelyreduce the vibration leakage of the resonator element 2F.

Also in the seventh embodiment, the same effects as in the firstembodiment described above can be achieved.

2. Resonator

Next, a resonator according to the invention will be described.

FIG. 15 is a plan view showing a resonator according to a preferredembodiment of the invention, and FIG. 16 is a cross-sectional view takenalong the line C-C of FIG. 15.

As shown in FIG. 15, a resonator 1 includes the resonator element 2(resonator element according to the invention) and a package 9 in whichthe resonator element 2 is housed. In addition, the resonator element 2is the same as the resonator element described in the first embodiment.

The package 9 includes a box-shaped base 91 having a recess 911, whichis opened on the top surface, and a plate-shaped lid 92 bonded to thebase 91 so as to close the opening of the recess 911. The package 9 hasa storage space formed by closing the recess 911 with the lid 92, andthe resonator element 2 is housed in the storage space in an airtightmanner. The resonator element 2 is fixed to the bottom surface of therecess 911 through a conductive adhesive 11, which is formed by mixing aconductive filler in an epoxy-based or acrylic resin, for example, inthe base portion 4. The storage space may be in a decompressed(preferably, vacuum) state, or inert gas, such as nitrogen, helium, andargon, may fill the storage space. In this case, the vibrationcharacteristics of the resonator element 2 are improved.

Materials of the base 91 are not limited in particular, and variousceramics, such as aluminum oxide, can be used. In addition, althoughmaterials of the lid 92 are not limited in particular, it is preferableto use a member having a linear expansion coefficient similar to that ofthe material of the base 91. For example, when the above-describedceramic is used as a material of the base 91, it is preferable to use analloy, such as Kovar. In addition, bonding of the base 91 and the lid 92is not limited in particular. For example, the base 91 and the lid 92may be bonded to each other through an adhesive or may be bonded to eachother by seam welding or the like.

In addition, connecting terminals 951 and 961 are formed on the bottomsurface of the recess 911 of the base 91. Although not shown, the firstdriving electrode 84 of the resonator element 2 is electricallyconnected to the connecting terminal 951 through a conductive adhesive11 in the base portion 4. Similarly, although not shown, the seconddriving electrode 85 of the resonator element 2 is electricallyconnected to the connecting terminal 961 through the conductive adhesive11 in the base portion 4.

In addition, the connecting terminal 951 is electrically connected to anexternal terminal 953, which is formed on the bottom surface of the base91, through a penetrating electrode 952 passing through the base 91, andthe connecting terminal 961 is electrically connected to an externalterminal 963, which is formed on the bottom surface of the base 91,through a penetrating electrode 962 passing through the base 91.

Materials of the connecting terminals 951 and 961, the penetratingelectrodes 952 and 962, and the external terminals 953 and 963 are notlimited in particular as long as the materials are electricallyconductive. For example, the connecting terminals 951 and 961, thepenetrating electrodes 952 and 962, and the external terminals 953 and963 may be formed of a metal coat that is formed by laminating a coat,such as Ni (nickel), Au (gold), Ag (silver), or Cu (copper), on ametalized layer (base layer), such as Cr (chromium) or W (tungsten).

3. Oscillator

Next, an oscillator to which the resonator element according to theinvention is applied (oscillator according to the invention) will bedescribed.

FIG. 17 is a cross-sectional view showing an oscillator according to apreferred embodiment of the invention.

An oscillator 10 shown in FIG. 17 includes a resonator 1 and an IC chip8 for driving the resonator element 2. Hereinafter, the oscillator 10will be described focusing on the differences from the resonatordescribed above, and explanation of the same matters will be omitted.

As shown in FIG. 17, the package 9 includes a box-shaped base 91 havinga recess 911 and a plate-shaped lid 92 for closing the opening of therecess 911. In addition, the recess 911 of the base 91 has a firstrecess 911 a opened on the top surface of the base 91, a second recess911 b opened in a middle portion of the bottom surface of the firstrecess 911 a, and a third recess 911 c opened in a middle portion of thebottom surface of the second recess 911 b.

Connecting terminals 95 and 96 are formed on the bottom surface of thefirst recess 911 a. In addition, the IC chip 8 is disposed on the bottomsurface of the third recess 911 c. The IC chip 8 includes an oscillationcircuit for controlling the driving of the resonator element 2. When theresonator element 2 is driven by the IC chip 8, it is possible toextract a signal of a predetermined frequency.

In addition, a plurality of internal terminals 93 electrically connectedto the IC chip 8 through a wire are formed on the bottom surface of thesecond recess 911 b. A terminal electrically connected to an externalterminal 94 formed on the bottom surface of the package 9 through a via(not shown) formed in the base 91, a terminal electrically connected tothe connecting terminal 95 through a via or a wire (not shown), and aterminal electrically connected to the connecting terminal 96 through avia or a wire (not shown) are included in the plurality of internalterminals 93.

In addition, although the configuration in which the IC chip 8 isdisposed in the storage space has been described in the configurationshown in FIG. 17, the arrangement of the IC chip 8 is not limited inparticular. For example, the IC chip 8 may be disposed outside thepackage 9 (disposed on the bottom surface of the base).

4. Electronic Apparatus

Next, an electronic apparatus to which the resonator element accordingto the invention is applied (electronic apparatus according to theinvention) will be described.

FIG. 18 is a perspective view showing the configuration of a mobile (ornotebook) personal computer as an electronic apparatus including theresonator element according to the invention. In FIG. 18, a personalcomputer 1100 is configured to include a main body 1104 having akeyboard 1102 and a display unit 1106 having a display section 2000, andthe display unit 1106 is supported so as to be rotatable with respect tothe main body 1104 through a hinge structure. The resonator element 2that functions as a filter, a resonator, a reference clock, and the likeis provided in the personal computer 1100.

FIG. 19 is a perspective view showing the configuration of a mobilephone (PHS is also included) as an electronic apparatus including theresonator element according to the invention. In FIG. 19, a mobile phone1200 includes a plurality of operation buttons 1202, an earpiece 1204,and a mouthpiece 1206, and a display section 2000 is disposed betweenthe operation buttons 1202 and the earpiece 1204. The resonator element2 that functions as a filter, a resonator, and the like is built intothe mobile phone 1200.

FIG. 20 is a perspective view showing the configuration of a digitalstill camera as an electronic apparatus including the resonator elementaccording to the invention. In addition, connection with an externaldevice is simply shown in FIG. 20. Here, a silver halide photograph filmis exposed to light according to an optical image of a subject in atypical camera, while a digital still camera 1300 generates an imagingsignal (image signal) by performing photoelectric conversion of anoptical image of a subject using an imaging element, such as a chargecoupled device (CCD).

A display unit is provided on the back of a case (body) 1302 in thedigital still camera 1300, so that display based on the imaging signalof the CCD is performed. The display unit functions as a viewfinder thatdisplays a subject as an electronic image. In addition, a lightreceiving unit 1304 including an optical lens (imaging optical system),a CCD, and the like is provided on the front side (back side in FIG. 20)of the case 1302.

When a photographer checks a subject image displayed on the display unitand presses a shutter button 1306, an imaging signal of the CCD at thatpoint in time is transferred and stored in a memory 1308. In addition,in the digital still camera 1300, a video signal output terminal 1312and an input/output terminal for data communication 1314 are provided onthe side surface of the case 1302. In addition, as shown in FIG. 20, atelevision monitor 1430 is connected to the video signal output terminal1312 and a personal computer 1440 is connected to the input/outputterminal for data communication 1314 when necessary. In addition, animaging signal stored in the memory 1308 may be output to the televisionmonitor 1430 or the personal computer 1440 by a predetermined operation.The resonator element 2 that functions as a filter, a resonator, and thelike is built into the digital still camera 1300.

In addition, the electronic apparatus including the resonator elementaccording to the invention can be applied not only to the personalcomputer (mobile personal computer) shown in FIG. 18, the mobile phoneshown in FIG. 19, and the digital still camera shown in FIG. 20 but alsoto an ink jet type discharge apparatus (for example, an ink jetprinter), a laptop type personal computer, a television, a video camera,a video tape recorder, a car navigation apparatus, a pager, anelectronic organizer (an electronic organizer with a communicationfunction is also included), an electronic dictionary, an electroniccalculator, an electronic game machine, a word processor, a workstation,a video phone, a television monitor for security, electronic binoculars,a POS terminal, medical equipment (for example, an electronicthermometer, a sphygmomanometer, a blood sugar meter, anelectrocardiographic measurement device, an ultrasonic diagnosticapparatus, and an electronic endoscope), a fish detector, variousmeasurement apparatuses, instruments (for example, instruments forvehicles, aircraft, and ships), a flight simulator, and the like.

5. Moving Object

Next, a moving object (moving object according to the invention) towhich the resonator element according to the invention is applied willbe described.

FIG. 21 is a perspective view schematically showing a vehicle as anexample of the moving object according to the invention. The resonatorelement 2 is mounted in a vehicle 1500. The resonator element 2 can bewidely applied to an electronic control unit (ECU), such as a keylessentry, an immobilizer, a car navigation system, a car air-conditioner,an anti-lock brake system (ABS), an airbag, a tire pressure monitoringsystem (TPMS), an engine control, a battery monitor of a hybrid vehicleor an electric vehicle, and a vehicle body position control system.

While the resonator element, the resonator, the oscillator, theelectronic apparatus, and the moving object according to the inventionhave been described with reference to the illustrated embodiments, theinvention is not limited thereto, and the configuration of each portionmay be replaced with an arbitrary configuration having the samefunction. In addition, other arbitrary structures may be added to theinvention. In addition, the embodiments described above may beappropriately combined.

The entire disclosure of Japanese Patent Application No. 2013-052489,filed Mar. 14, 2013 is expressly incorporated by reference herein.

What is claimed is:
 1. A resonator element, comprising: a base portion;and a pair of vibrating arms that extend in a first direction from thebase portion in plan view and are aligned along a second directioncrossing the first direction in plan view, each of the vibrating armsincluding: an arm portion; and a wide portion disposed on a side of thearm portion opposite to the base portion in plan view and having alength along the second direction that is greater than the arm portionin plan view, wherein for each vibrating arm: a length of the vibratingarm along the first direction is L and a length of the wide portionalong the first direction is H, a relationship of 1.2%<H/L<30.0% issatisfied, a length of the arm portion along the second direction is W1and a length of the wide portion along the second direction is W2, arelationship of 1.5≦W2/W1≦10.0 is satisfied, and 12.8 μm≦W1≦50 μm. 2.The resonator element according to claim 1, wherein for each vibratingarm the L and the H satisfy a relationship of 4.6%<H/L<22.3%.
 3. Theresonator element according to claim 1, wherein for each vibrating armthe W1 and the W2 satisfy a relationship of 1.6≦W2/W1≦7.0.
 4. Theresonator element according to claim 1, wherein for each vibrating arm abottomed groove extending along the first direction is provided on aprincipal surface of the arm portion.
 5. The resonator element accordingto claim 1, wherein for each vibrating arm the wide portion includes amain body, which is connected to a side of the arm portion opposite tothe base portion, and a protruding portion, which extends from the mainbody toward the base portion of the arm portion so as to be spaced apartfrom the arm portion in plan view.
 6. The resonator element according toclaim 5, wherein for each vibrating arm the wide portion furtherincludes a connecting portion that is located in a region interposedbetween the protruding portion and the arm portion, connects theprotruding portion and the arm portion to each other, and has a lengthalong a third direction perpendicular to the first and second directionsthat is smaller than the arm portion and the protruding portion.
 7. Theresonator element according to claim 1, wherein the base portionincludes a width-decreasing portion, in which a length in the seconddirection gradually decreases as a distance from the vibrating armincreases, on a side opposite to a side where the vibrating arm extends.8. The resonator element according to claim 1, further comprising: asupport portion that is disposed between the pair of vibrating arms andextends from the base portion.
 9. The resonator element according toclaim 1, further comprising: a pair of support arms that are connectedto the base portion, the pair of vibrating arms being interposed betweenthe pair of support arms in plan view.
 10. A resonator, comprising: theresonator element according to claim 1; and a package in which theresonator element is housed.
 11. A resonator, comprising: the resonatorelement according to claim 2; and a package in which the resonatorelement is housed.
 12. An oscillator, comprising: the resonator elementaccording to claim 1; and an oscillation circuit electrically connectedto the resonator element.
 13. An oscillator, comprising: the resonatorelement according to claim 2; and an oscillation circuit electricallyconnected to the resonator element.
 14. An electronic apparatus,comprising: the resonator element according to claim
 1. 15. Anelectronic apparatus, comprising: the resonator element according toclaim
 2. 16. A moving object, comprising: the resonator elementaccording to claim
 1. 17. A moving object, comprising: the resonatorelement according to claim 2.